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Convergence and rate of approximation in $BV^{\varphi}(\mathbb{R}^N_+)$ for a class of Mellin integral operators

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Laura Angeloni, Gianluca Vinti

Functional Analysis · Submitted 26 Aug 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb{R}^N_+)$.

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arXiv ID1408.6168 (version 1)
Pith IDDZY7LWBZ, Pith's permanent record of this paper and its review
CitationGianluca Vinti, Laura Angeloni. "Convergence and rate of approximation in $BV^{\varphi}(\mathbb{R}^N_+)$ for a class of Mellin integral operators." arXiv:1408.6168 (2014). https://pith.science/paper/DZY7LWBZ
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,434 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb{R}^N_+)$. Here $BV^{\varphi}(\mathbb{R}^N_+)$ denotes the space of functions with bounded $\varphi-$variation on $\mathbb{R}^N_+$, defined by means of a concept of multidimensional $\varphi-$variation in the sense of Tonelli.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb{R}^N_+)$. contribution 1.00 0.85 0.23 asserted 0.88
s1 Here $BV^{\varphi}(\mathbb{R}^N_+)$ denotes the space of functions with bounded $\varphi-$variation on $\mathbb{R}^N_+$, defined by means of a concept of multidimensional $\varphi-$variation in the sense of Tonelli. background 0.94 0.17 0.03 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb{R}^N_+)$. Here $BV^{\varphi}(\mathbb{R}^N_+)$ denotes the space of functions with bounded $\varphi-$variation on $\mathbb{R}^N_+$, defined by means of a concept of multidimensional $\varphi-$variation in the sense of Tonelli.

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